We present reduced-order models of unsteady low-Mach-number ideal gas flows in two-dimensional rectangular microchannels subject to first-order slip-boundary conditions. The pressure and density are related by a polytropic process, allowing for isothermal or isentropic flow assumptions. The Navier–Stokes equations are simplified using low-Mach-number expansions of the pressure and velocity fields. Up to first order, this approximation results in a system that is subject to no-slip condition at the solid boundary. The second-order system satisfies the slip-boundary conditions. The resulting equations and the subsequent pressure-flow-rate relationships enable modeling the flow using analog circuit components. The accuracy of the proposed models is investigated for steady and unsteady flows in a two-dimensional channel for different values of Mach and Knudsen numbers.
Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows
Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received September 5, 2013; final manuscript received November 27, 2013; published online March 10, 2014. Assoc. Editor: Daniel Attinger.
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Issa, L., and Lakkis, I. (March 10, 2014). "Reduced-Order Modeling of Low Mach Number Unsteady Microchannel Flows." ASME. J. Fluids Eng. May 2014; 136(5): 051201. https://doi.org/10.1115/1.4026199
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